Lecture 6: Integrated Circuit Resistors

1. Lecture 6: Integrated Circuit Resistors Prof. Niknejad

2. Lecture Outline • Semiconductors • Si Diamond Structure • Bond Model • Intrinsic Carrier Concentration • Doping by Ion Implantation • Drift • Velocity Saturation • IC Process Flow • Resistor Layout • Diffusion University of California, Berkeley

3. Resistivity for a Few Materials • Pure copper, 273K 1.56×10-6 ohm-cm • Pure copper, 373 K 2.24×10-6 ohm-cm • Pure germanium, 273 K 200 ohm-cm • Pure germanium, 500 K .12 ohm-cm • Pure water, 291 K 2.5×107 ohm-cm • Seawater 25 ohm-cm What gives rise to this enormous range? Why are some materials semi-conductive? Why the strong temp dependence? University of California, Berkeley

4. (1s)2 (2s)2 (3sp)4 (2p)6 Hybridized State Electronic Properties of Silicon • Silicon is in Group IV • Atom electronic structure: 1s22s22p63s23p2 • Crystal electronic structure: 1s22s22p63(sp)4 • Diamond lattice, with 0.235 nm bond length • Very poor conductor at room temperature: why? University of California, Berkeley

5. Periodic Table of Elements University of California, Berkeley

6. The Diamond Structure 3sp tetrahedral bond University of California, Berkeley

7. . . . E3 Allowed Energy Levels E2 Energy Forbidden Band Gap E1 Atomic Spacing Lattice Constant States of an Atom • Quantum Mechanics: The allowed energy levels for an atom are discrete (2 electrons can occupy a state since with opposite spin) • When atoms are brought into close contact, these energy levels split • If there are a large number of atoms, the discrete energy levels form a “continuous” band University of California, Berkeley

8. Conduction Band Valence Band Conduction Band band gap Valence Band Electrons can gain energy from lattice (phonon) or photon to become “free” Energy Band Diagram • The gap between the conduction and valence band determines the conductive properties of the material • Metal • negligible band gap or overlap • Insulator • large band gap, ~ 8 eV • Semiconductor • medium sized gap, ~ 1 eV e- e- University of California, Berkeley

9. + + + + + + + + + + + + + + + + + + + + + + + + Model for Good Conductor • The atoms are all ionized and a “sea” of electrons can wander about crystal: • The electrons are the “glue” that holds the solid together • Since they are “free”, they respond to applied fields and give rise to conductions On time scale of electrons, lattice looks stationary… University of California, Berkeley

10. Bond Model for Silicon (T=0K) Silicon Ion (+4 q) 2 electrons in each bond Four Valence Electrons Contributed by each ion (-4 q) University of California, Berkeley

11. Bond Model for Silicon (T>0K) • Some bond are broken: free electron • Leave behind a positive ion or trap (a hole) + - University of California, Berkeley

12. Holes? • Notice that the vacancy (hole) left behind can be filled by a neighboring electron • It looks like there is a positive charge traveling around! • Treat holes as legitimate particles. + - University of California, Berkeley

13. Yes, Holes! • The hole represents the void after a bond is broken • Since it is energetically favorable for nearby electrons to fill this void, the hole is quickly filled • But this leaves a new void since it is more likely that a valence band electron fills the void (much larger density that conduction band electrons) • The net motion of many electrons in the valence band can be equivalently represented as the motion of a hole University of California, Berkeley

14. More About Holes • When a conduction band electron encounters a hole, the process is called recombination • The electron and hole annihilate one another thus depleting the supply of carriers • In thermal equilibrium, a generation process counterbalances to produce a steady stream of carriers University of California, Berkeley

15. Thermal Equilibrium (Pure Si) • Balance between generation and recombination determines no = po • Strong function of temperature: T = 300 oK University of California, Berkeley

16. + Doping with Group V Elements • P, As (group 5): extra bonding electron … lost to crystal at room temperature Immobile Charge Left Behind University of California, Berkeley

17. Free Electrons Ions (Immobile) Free Holes Donor Accounting • Each ionized donor will contribute an extra “free” electron • The material is charge neutral, so the total charge concentration must sum to zero: • By Mass-Action Law: University of California, Berkeley

18. Donor Accounting (cont) • Solve quadratic: • Only positive root is physically valid: • For most practical situations: University of California, Berkeley

19. Doping with Group III Elements • Boron: 3 bonding electrons  one bond is unsaturated • Only free hole … negative ion is immobile! - University of California, Berkeley

20. Mass Action Law • Balance between generation and recombination: • N-type case: • P-type case: University of California, Berkeley

21. + Compensation • Dope with both donors and acceptors: • Create free electron and hole! - - + University of California, Berkeley

22. Compensation (cont.) • More donors than acceptors: Nd > Na • More acceptors than donors: Na > Nd University of California, Berkeley

23. (hole case) x Thermal Equilibrium Rapid, random motion of holes and electrons at “thermal velocity” vth = 107 cm/s with collisions every c = 10-13 s. Apply an electric field Eand charge carriers accelerate … for c seconds University of California, Berkeley

24. Drift Velocity and Mobility For holes: For electrons: University of California, Berkeley

25. Mobility vs. Doping in Silicon at 300 oK “default” values: University of California, Berkeley